Since all circles are similar, a proportion can be set up using the circumference and diameter of each circle. Substitute the values d1 = 1, C1 = π, and d2 = 2r into the proportion.

StartFraction C 1 Over d 1 EndFraction = StartFraction C 2 Over d 2 EndFraction

Which shows how to correctly solve for C2, the circumference of any circle with radius r?

A. Because StartFraction pi Over 1 EndFraction = StartFraction C 2 Over 2 r EndFraction , C 2 = 2 r pi

B. Because StartFraction 1 Over pi EndFraction = StartFraction C 2 Over 2 r EndFraction ,
2 = StartFraction 2 r Over pi EndFraction

C. Because StartFraction pi Over 2 r EndFraction = StartFraction C 2 Over 1 EndFraction , C 2 = StartFraction pi Over 2 r EndFraction

D. Because StartFraction pi Over 1 EndFraction = StartFraction C 2 Over 4 r EndFraction , C 2 = 4 r pi

Answer:

x^2-9x+8

Step-by-step explanation:

(2x^2-5x+3)-(-x^2+4x-5)

Open the bracket first

2x^2-5x+3+x^2-4x+5

Collect like terms

2x^2+x^2-5x-4x+3+5

x^2-9x+8

So the final answer is x^2-9x+8

Answer:

5

Step-by-step explanation:

According to the question, A cone frustum is inscribed in a sphere of radius 13. If one of the bases of the frustum is a great circle of the sphere, and the other base has radius 12.We are now asked to find the height of the frustum.

---The height of this frustum is equal to the distance of its smaller base from the center of the sphere.

Therefore,it is assigned the pattern

H = √(r1² - r2²

Where r1 is the radius of the sphere

And r2 is the radius of the other base of the frustum

H is the height that we are looking for

H = √(13² - 12²)

= √( 169 - 144 )

= √ 25

H = 5

Final answer:

The height of the frustum inscribed in a sphere with a radius of 13 and one base having a radius of 12 is found to be 10 units using the Pythagorean theorem.

Explanation:

To find the height of the frustum inscribed in a sphere of radius 13, where one base is a great circle of the sphere, and the other base has radius 12, we can use geometry and Pythagorean theorem.

Consider the right triangle formed by the radius of the sphere, half of the frustum height (since the center of the sphere is midway of the frustum's height for the configuration given), and the radius of the smaller base of the frustum.

The radius of the sphere is 13, and the radius of the smaller base is 12.

Using the Pythagorean theorem (a² + b² = c²), we can find the half-height of the frustum.

So, we have:

122 + b² = 132

144 + b² = 169

b² = 25 => b = 5

Thus, the full height (h) of the frustum is 10 units.

To determine the time necessary for an investment to grow from $9,500 to $12,600 at an interest rate of 5.75% compounded quarterly, the compound interest formula is rearranged and solved for time, yielding approximately 6.6 years.

To find out how long it takes for an investment to grow from $9,500 to $12,600 with an interest rate of 5.75% compounded quarterly, we use the formula for compound interest: A = P(1 + r/n)^(nt), where:

In this case, we're solving for t, so we rearrange the formula: t = ln(A/P) / (n * ln(1 + r/n)). Substituting the provided values:

Thus, t = ln(12600/9500) / (4 * ln(1 + 0.0575/4)). After calculating, we find that t ≈ 6.6 years, rounded to the nearest tenth of a year.

The person must leave the money in the bank for approximately 5.4 years until it reaches $12600, with interest compounded quarterly.

To find out how long it takes for the investment to reach $12600 at a 5.75% interest compounded quarterly, we can use the formula for compound interest:

[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]

Where:

- A is the amount of money accumulated after t  years, including interest.

- P is the principal amount (the initial amount of money).

- r is the annual interest rate (in decimal).

- n is the number of times interest is compounded per year.

- t is the time the money is invested for, in years.

We want to find t, so we can rearrange the formula to solve for t:

[tex]\[ t = \frac{\log\left(\frac{A}{P}\right)}{n \cdot \log\left(1 + \frac{r}{n}\right)} \][/tex]

Given:

- P = 9500

- A = 12600

- r = 0.0575  (5.75% expressed as a decimal)

- n = 4 (quarterly compounding)

Substituting these values into the formula:

[tex]\[ t = \frac{\log\left(\frac{12600}{9500}\right)}{4 \cdot \log\left(1 + \frac{0.0575}{4}\right)} \][/tex]

[tex]\[ t = \frac{\log\left(\frac{12600}{9500}\right)}{4 \cdot \log\left(1 + 0.0575/4\right)} \]\[ t \approx \frac{\log(1.32631579)}{4 \cdot \log(1.014375)} \]\[ t \approx \frac{0.12224324}{4 \cdot 0.00570388} \]\[ t \approx \frac{0.12224324}{0.02281552} \]\[ t \approx 5.361 \][/tex]

Rounded to the nearest tenth, it takes approximately 5.4 years for the investment to reach $12600 at 5.75% interest compounded quarterly.

Answer:

93 students

Step-by-step explanation:

Answer:

266-----------35%

x----------------100%

x=(266 * 100%) / 35%= 760

There are 760 students in the middle school

Step-by-step explanation:

We solve this problem by the rule of three.

Answer: c

Step-by-step explanation:

[tex]x^2+4x-45[/tex]

[tex](x+9)(x-5)[/tex]

Answer:

c

Step-by-step explanation:

Answer:

4/15 = 0.266666%

Step-by-step explanation:

Answer:

a^n=-9+(n-1).5

Step-by-step explanation:

Arithmetic sequence=a+(n-1)d

a=-9

n=?

d=+5

Arithmetic sequence=-9+(n-1)5

=-9+5n-5

Collect like terms

-9-5+5n

-14+5n

So the final answer is

an=-9+(n-1).5

Answer:

No

Step-by-step explanation:

Answer: 825 minutes

Step-by-step explanation: We know there is a total of 15 people in the book club. We also know that 10 people each read an average of 65 minutes each day, and the remaining 5 people read for an average of 35 minutes each day.

To find the total amount f minutes read, simply multiply the amount of people by the minutes read.

10 x 65 = 650 total minutes read if 10 people each read 65 minutes for one day.

5 x 35 = 175 total minutes read if 5 people each read for 35 minutes in one day.

Now, simply add the total minutes read to find the reading time fr the entire book club each day.

650 + 175 = 825 average reading time for the entire book club each day.

I'm guessing there's a menu of choices to go with this one, and we just need to try (-2,9) with each choice.  But it's a much more interesting problem without the menu.

First we verify (-2,9) is on the line y=-7x-5,

-7(-2)-5 = 14-5 = 9, good.

There's a whole family of possibilities for the second equation, basically all the other lines through (-2,9).  Believe it or not, that's called a pencil of lines. We need two parameters a and b, whose values only matter in ratio, to represent all these.  If we tried to do it with just the slope we'd miss one line, the vertical line x=-2.

We'll do the line through (-2,9) and (a,b).  A little thought tells us it's

(a + 2)(y - 9) = (b - 9)(x + 2)

When we plug in (-2,9) we get 0=0, good.  When we plug in (a,b) we get

(a + 2)(b - 9) = (b - 9)(a + 2)

which is also true.

(a + 2)(y - 9) = (b - 9)(x + 2)

(b - 9)x - (a+2)y = -9(a + 2)  - 2(b-9)

(b - 9)x - (a+2)y =  -9a - 2b

We can choose any a and b and we'll get the line through (-2,9) and (a,b), so it will have a solution (-2,9) where it meets y = -7x - 5.

We need to make sure (a,b) isn't already on  y = -7x - 5 which is the same line twice.

For arbitrary a,b,  b ≠ -7a - 5, the lines y = -7x - 5  and

(b - 9)x - (a+2)y =  -9a - 2b

meet at exactly one point, namely (-2,9)

Let's generate a few and plot.  We'll do a vertical and horizontal an a couple of others.  

a=-2, b=0,     (b - 9)x - (a+2)y =  -9a - 2b

-9x = 18

x = -2

a=0, b=9,    (b - 9)x - (a+2)y =  -9a - 2b

-2y = -18

y = 9

a=1, b=1,    (b - 9)x - (a+2)y =  -9a - 2b

-8x - 3y = -11

a=1, b=3,    (b - 9)x - (a+2)y =  -9a - 2b

-6x - 3y = -15

2x + y = 5

plot y=-7x+5, x = -2, y = 9, -8x - 3y = -11, 2x - y = 5

Answer:

8x+8

Step-by-step explanation:

The perimeter is all the sides added together:

3x+2+6x-1+7-x = 8x+8

The perimeter of the triangle in terms of x is expressed as 8 ( x - 1 ).

Given,

The sides of a triangle are 3x+2, 6x-1, and 7-x.

We need to express the perimeter of the triangle in terms of x.

It is given by:

Perimeter = sum of all three sides.

Find the sides of a triangle.

We have,

One side = 3x + 2

Second side = 6x - 1

Third side = 7 - x

Find the perimeter of the triangle.

Perimeter:

= one side + second side + third side

= (3x + 2) + (6x - 1) + (7 - x)

= 3x + 2 + 6x - 1 + 7 - x

= 3x + 6x - x + 2 - 1 + 7

= 8x + 8

Taking 8 common

= 8 ( x - 1 )

Thus the perimeter of the triangle in terms of x is expressed as 8 ( x - 1 ).

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Answer:

13.05 l

Step-by-step explanation:

For 12 liter of water 12/4 times 0.35 l concentrate has to be added.

The total liquid volume is then

12 + 12/4 * 0.35 = 13.05

(1 cl = 0.01 l)

Answer:

3.5l

Step-by-step explanation:

Answer:r= 2.26 inches

Step-by-step explanation:

Answer: r=4inches

Step-by-step explanation:

Volume of a cone= pir2h/3

Pi= 3.14

R=?

H=18

V=96pi

Substitute for the values

V=pir2h/3

96pi=pir218/3

Pi will cancel pi out

So we have

96=r218/3

Cross multiply

R2=96×3/18

R2=16

R=square root of 16

R=4inches

The radius is 4inches

Answer:

12

Step-by-step explanation:

Answer:

D (-4,2)

Step-by-step explanation:

The coordinates of F is (-4,2), the correct option is D.

A parallelogram is a polygon with four sides, the opposite sides of the parallelogram is equal and parallel.

The figure is attached with the answer.

The final image is obtained by series of Transformations

1. Translation (1,2)

Translation T₁,₂ is (x,y)→(x+1,y+2)

So, After translation from F to F' the point  F' = (x+1,y+2)

2. After Reflection along y axis F" = (-(x+1), y+2)

F" = ( 3,4)

F' = (-3,4)

F = (-4 , 2)

Therefore, the coordinates of F is (-4,2), the correct option is D.

The missing figure is attached with the answer.

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Answer:

^3(square root symbol) x^4 this is for radicals only

Step-by-step explanation:

If you are doing fractions then the correct answer would be x1 1/3

Explanation for ^3(square root symbol) x^4

When writing these in radicals simplified x^4/3 you put the denominator over your square root, and your numerator will be squared by your denominator. But your numerator must be to x as x is the constant. So ^3(square root symbol) x^4 = x^4/3

Explanation for x1 1/3

When simplifying fractions you take out the extra of the fraction and turn it into its own fraction, and the whole fraction you are left with, in this case being 3/3, you turn into a whole number, which is 1, and you add your left over fraction, 1/3, and put them together 1 1/3, but don't forget your x, x1 1/3

The expression 'x 4/3' can alternatively be written as the cube root of x to the fourth power, expressed as ∛[tex](x^4)[/tex]a mathematical context.

The statement x 4/3 is a mathematical expression which can be interpreted in different ways based on context.

If the intention is to write the expression x to the power of 4/3, it can be expressed as a radical, specifically as the cube root of x4.

The cube root operation can be represented by the radical symbol, so the alternative way to write it would be ∛(x4).

This would not be a Unit Conversion question. It is essential to understand that without further context, the expression is ambiguous and might represent other mathematical operations or concepts.

However, it does not seem to relate directly to any of the extraneous information provided.

Answer:

2412

Step-by-step explanation:12*12*13=1872 15*12*3=540 1872+540=2412

Answer:

[tex]B_2=4\pi r^2[/tex]

Step-by-step explanation:

we know that

The area of the base of a cylinder is given by the formula

[tex]B=\pi r^{2}[/tex]

where

r is the radius of the circular base

If the radius is doubled

then

[tex]r=2r[/tex]

The new base area is

[tex]B_2=\pi (2r)^{2}\\B_2=4\pi r^2[/tex]

so

[tex]B_2=4B[/tex]

therefore

The new area of the base is 4 times the area of the original base

Answer:

r2+A

Step-by-step explanation:

lalalalalalalalalalalalala

Answer:

Bulldogs

Cardinals

Tornado

Step-by-step explanation:

Cardinals: 31 injuries

Tornado: 31 injuries

Bulldogs : 17 injuries

I think I did this right and i counted them twice, but they are the same so it doesn't matter where you put them and if this is wrong then im sorry but i counted them several times. If this is right can I get a brainliest?

Answer:

Step-by-step explanation:

Spinner A

Spinner B

Probability of both A and B land on red:

Number of attempts to get outcome of 84 red on both spinners is:

Probability of both spinners land on blue:

Estimated number of both spinners land on blue:

The estimated number of times that both spinners will land on blue is 56 times. This was calculated based on the number of times both spinners land on red and the probabilities of each spinner landing on blue.

This problem deals with the subject of probability. Since we know that the number of times both spinners (A and B) land on red is 84, we can use this as a base to find the probability for each to land on blue.

The probability of spinner A landing on red is 0.5, therefore the probability of it landing on blue will also be 0.5 (1-0.5=0.5). Similarly, the probability of spinner B landing on red is 0.6, thus the probability of it landing on blue is 0.4 (1-0.6=0.4).

To get the overall probability of both spinners landing on blue, we multiply the probabilities for each individual spinner. Hence, the overall probability is 0.5 * 0.4 = 0.2.

Finally, to find the estimated number of times both spinners will land on blue, we can divide the number of times both spinners land on red (84) by the ratio of the probability for both landing on blue to the probability for both landing on red, yielding an estimate of 84 * (0.2 / 0.3) = 56 times.

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Answer:

D

Step-by-step explanation:

For some side lengths to create a triangle, any two of the side lengths must have an added length together of less than the third leg. Otherwise, the vertices would simply not be able to be connected by the lines. In a), 3+5=8, but since it is not more, the triangle will not be able to be formed (it would basically just be a line.) In B, 7+8< 16. In C, there is the same situation as with the first example (4+15=19). Finally, in the last one, 5+7>12, and all of the side lengths work out. Therefore, the correct answer is D. Hope this helps!

Answer:

Step-by-step explanation:

10 gets carried down.

The value of A in A(x² + 4x) = 13 that gives 10x² + 40x - 13 = 0 is 10.

A quadratic function is in the form:

y = ax² + bx + c

Given that:

10x² + 40x - 13 = 0

Solving using completing the square:

10x² + 40x = 13

10(x² + 4x) = 13

The value of A in A(x² + 4x) = 13 that gives 10x² + 40x - 13 = 0 is 10.

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Answer:

14.1 in³

Step-by-step explanation:

Volume of sphere:

(4/3) × pi × r³

(4/3) × (22/7) × 1.5³

= 14.1428571426 in³

Answer:

14.1 cubic inch

Step-by-step explanation:

[tex]volume \: of \: knob \\ = \frac{4}{3} \pi {r}^{3} \\ = \frac{4}{3} \times 3.14 \times {1.5}^{3} \\ = \frac{4}{3} \times 3.14 \times 3.375 \\ = \frac{4}{3} \times 10.5975\\ = \frac{42.39}{3} \\ = 14.13 \: {inch}^{3} \\= 14.1 \: {inch}^{3} \\ [/tex]

Answer:

Step-by-step explanation:

To solve this

We have

Let the number think of b x

Three subtracted from the number will be

x-3

Then multiply by 4

4(x-3)

Open d brackets

4x-12

According to the given statement the expression will be "4x-12".

Let,

When "3" is subtracted from the number "x", we get

→ [tex]x-3[/tex]

and,

When "x-3" is multiply by "4", we get

→ [tex]4(x-3)[/tex]

After solving the brackets, we get    

→ [tex]4x-12[/tex]

Thus the answer above is correct.

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[tex]a_n=\frac{a_{n-1}+a_{n+1}}{2} \\a_n=\frac{-8+(-9)}{2} =-8,5[/tex]

/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\

P.S. Hello from Russia :^)

Final answer:

The arithmetic mean An between A(n-1) = -8 and A(n+1) = -9 is calculated by taking the average of these two terms, resulting in An = -8.5.

Explanation:

To find the arithmetic mean An between A(n-1) and A(n+1), we use the definition of the arithmetic mean for a sequence of numbers. The mean of two numbers is simply the sum of those numbers divided by two, which can be represented by the formula: mean = (a + b) / 2. Given A(n-1) = -8 and A(n+1) = -9, we can set up the formula as follows:

An = (A(n-1) + A(n+1)) / 2

Substituting the given values results in:

An = (-8 + (-9)) / 2

An = (-17) / 2

An = -8.5

Therefore, the arithmetic mean An of the given terms is -8.5.

Answer:

P (-1 , 0)

Step-by-step explanation:

M (-6 , 2)      N (9 , -4)     P (x , y)

horizontal distance of M and N = 9 - (-6) = 15

vertical distance of M and N = 2 - (-4) = 6

1/3 from x coordinate of M (-6): -6 + 15/3 = -1    This is x coordinate of point P

1/3 from y coordinate of M (2): 2 - 6/3 = 0    This is y coordinate of point P

P (x , y)  i.e P (-1 , 0)

check: distance of MP = √(-1 - (-6))² + (0 - 2)² = √29 = 5.385

distance of PN = √(-1 - 9)² + (0 - (-4))² = √116 = 10.77

MP / PN = 5.385 / 10.77 = 0.5 = 1/2

The values of x and y that partition the line segment MN into the ratio 1:2 are x = 3 and y = -4.

To determine the values of x and y that partition the line segment MN into the ratio MP:PN = 1:2, we can use the section formula. The section formula states that the coordinates of a point P(x,y) that partitions a line segment with endpoints M(x1, y1) and N(x2, y2) into the ratio m: n are given by:

x = (nx1 + mx2) / (m + n)

y = (ny1 + my2) / (m + n)

In this case, M(-6, 2) and N(9, -4), and the ratio is 1:2. Plugging these values into the section formula, we get:

x = (2*9 + 1*(-6)) / (1 + 2) = 3

y = (-4*2 + 2*(-4)) / (1 + 2) = -4

Therefore, the values of x and y that partition the line segment MN are x = 3 and y = -4.

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Answer:

Vijay cannot fit all the cubes into the box, he can only fit 20 cubes into the box

10 x 2 = 20 cubes

He would need 5 boxes to fit all the cubes

Hope this helps <3

The 5 th term of the given expression is 330[tex](6x)^{7}( 6y)^{4}[/tex].

Step-by-step explanation:

Given,

[tex](6x+6y)^{11}[/tex]

To find the 5th term of the given expression.

Formula

In a binomial series [tex](a+b)^{n}[/tex], the r th term is = nC(r-1) [tex]a^{n-r-1} b^{r-1}[/tex], where,

nC(r-1) = [tex]\frac{n!}{(r-1)!(n-r+1)!}[/tex]

Now,

Putting, n=11, r = r, a=6x and b=6y we get,

5 th term = 11C4[tex](6x)^{7}( 6y)^{4}[/tex]

= [tex]\frac{11!}{4!7!}[/tex][tex](6x)^{7}( 6y)^{4}[/tex]

= [tex]\frac{11X10X9X8X7!}{7!X4X3X2X1}[/tex][tex](6x)^{7}( 6y)^{4}[/tex]

= 330[tex](6x)^{7}( 6y)^{4}[/tex]

Here is the answer.

Answer:                      Received cold medicine  Did not receive cold medicine

Cold lasted longer than 7 days             23                                 20

Cold did not last longer than 7 days     27                                30

Step-by-step explanation:

i hope it helps

To complete the two-way frequency table, calculate the values for each cell based on the given information.

To complete the two-way frequency table, we need to fill in the missing values. Given that there are 100 participants in total, we can calculate the value for each cell. Starting with the top left cell, which represents participants who received the cold medicine and had their cold last longer than 7 days, the value would be 27. Similarly, we can calculate the values for the other cells in the table.

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